Errors in optically transmitted data are caused by a number of different factors, including distortion of optical signals in the air. In free-space optical communications systems that propagate optical signals through air, turbulence can be a significant source of channel impairment. For example, anomalous refraction of an optical beam (e.g., scintillation) can be caused by small-scale fluctuations in air density that result from temperature or pressure gradients along the path of the optical beam. These atmospheric fluctuations can cause frequency-nonselective fades in the optical beam's power. The fade process has a correlation time which is typically much longer than the duration of a typical symbol in the optical beam, therefore reducing the signal-to-noise ratio of the data stream.
To reduce the effects of optical beam fading, some conventional technologies apply channel equalization and forward error correction (FEC) coding at the physical layer. Channel equalization is used to reduce the inter-symbol interference that is induced by band-limiting in the receiver or channel. Forward error correction at the physical layer introduces a structured redundancy on the transmitted symbol sequence that can be exploited at the receiver to correct errors in recovering the transmitted data due to channel impairments. However, the complexity associated with encoding and decoding a physical layer with a FEC code increases with the length of the codeword. For example, in high data rate systems, a codeword should span multiple channel coherence times to enable recovery of the symbols lost due to optical beam fading. However, such a codeword would be prohibitively complex to handle in many practical situations.
With other conventional technologies, lost data may be retransmitted from a transmitter to a receiver upon detecting data loss (e.g., a dropped data frame). However, in many cases, the additional round-trip latency caused by the re-transmission requests and the need for an additional feedback channel make these technologies impractical or undesirable.
Another conventional approach to mitigate fading relies on spatial diversity. Since turbulence has a transverse correlation length r0, if two optical source beams are separated by a distance D, then their fades will become statistically independent when D>>r0. Therefore, turbulence-induced errors in the optical beam (e.g., scintillation) are sufficiently non-correlated for optical beams that are spaced sufficiently apart. A conventional technology that utilizes spatial diversity to mitigate turbulence is called multi-beaming. The multi-beaming technique includes sending the same symbol along different paths separated by D, where D>>r0, such that different paths experience statistically independent fades and phase offsets. In this scenario, the total received signal intensity is the sum of several independent optical beams, each characterized by independent fading processes. As a result, the total received signal will thus have a smaller optical beam fading. However, this approach is only suitable when information is encoded by intensity, but is not applicable when the optical phase carries information. Accordingly, there remains a need for improved technique for the transmission of optical data at high data rates and low latency of the data transmission.